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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 313 · 40 sums
TalentJR

The method (Pairs make squares): Square: n × n. Quick way: (a + b)² = a² + 2ab + b², e.g. 42² = 1600 + 160 + 4. Square root: the number that times itself gives the square; a square ending in 4 has a root ending in 2 or 8. Make a perfect square: break into primes; multiply (or divide) by the prime left without a partner. 1 + 3 + 5 + … (n odd numbers) = n². Between n² and (n + 1)² there are 2n whole numbers.

NameDateTime takenScore ___ / 40
  1. 1.What is the smallest whole number by which 396 must be divided to get a perfect square?
  2. 2.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  3. 3.Which of these is a perfect square? (a) 127 (b) 121 (c) 135
  4. 4.A square garden has an area of 2209 square m. How long is each side (in m)?
  5. 5.What is 17²? =
  6. 6.What is the smallest whole number by which 704 must be divided to get a perfect square?
  7. 7.How many whole numbers lie between 23² and 24²?
  8. 8.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is √1849? =
  11. 11.What is 80²? =
  12. 12.Which of these is a perfect square? (a) 548 (b) 529 (c) 573
  13. 13.What is the smallest whole number by which 27 must be divided to get a perfect square?
  14. 14.What is √3136? =
  15. 15.What is 71²? =
  16. 16.How many whole numbers lie between 14² and 15²?
  17. 17.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
  18. 18.A square garden has an area of 2916 square m. How long is each side (in m)?
  19. 19.What is √3364? =
  20. 20.A square garden has an area of 289 square m. How long is each side (in m)?
  21. 21.Which of these is a perfect square? (a) 115 (b) 100 (c) 106
  22. 22.What is 35²? =
  23. 23.What is √441? =
  24. 24.How many whole numbers lie between 36² and 37²?
  25. 25.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  26. 26.How many whole numbers lie between 17² and 18²?
  27. 27.Which of these is a perfect square? (a) 1275 (b) 1225 (c) 1242
  28. 28.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
  30. 30.What is √484? =
  31. 31.A square garden has an area of 169 square m. How long is each side (in m)?
  32. 32.A square garden has an area of 1600 square m. How long is each side (in m)?
  33. 33.What is √5776? =
  34. 34.A square garden has an area of 100 square m. How long is each side (in m)?
  35. 35.How many whole numbers lie between 10² and 11²?
  36. 36.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
  38. 38.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  39. 39.How many whole numbers lie between 28² and 29²?
  40. 40.What is √1156? =

Answer key

  1. 11
  2. 15
  3. 121
  4. 47
  5. 289
  6. 11
  7. 46
  8. 81
  9. 196
  10. 43
  11. 6400
  12. 529
  13. 3
  14. 56
  15. 5041
  16. 28
  17. 324
  18. 54
  19. 58
  20. 17
  21. 100
  22. 1225
  23. 21
  24. 72
  25. 49
  26. 34
  27. 1225
  28. 625
  29. 15
  30. 22
  31. 13
  32. 40
  33. 76
  34. 10
  35. 20
  36. 729
  37. 2
  38. 3
  39. 56
  40. 34

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